Koszulity in the category $\mathcal{O}$ of the periplectic Lie Superalgebra $\mathfrak{pe}(2)$

The main result of this paper is to establish precisely which blocks in the Category $\mathcal{O}$ of the periplectic Lie superalgebra $\mathfrak{pe}(2)$ are Koszul. It is known that $\mathcal{O}(\mathfrak{pe}(2))$ has three blocks up to equivalence; one generic block and two integral blocks. The ge